If I send some bitcoins to some address, and I pay the proper fees, how sure am I that it will be included in the next block? Are there any guarantees if I want my payment to be included in the next block that is mined?
Actually just pay recommend fees you can get your transaction sent less than 10minutes. Guaranteed

is there no limit to the number of transactions in a block? what if everybody pays recommended fees? so some will still not make it? am i right?
there is a limit to that. more transaction means more size, and the block size are limited to 1mb
as of now does the 1 mb limit always get full?
according to this
https://blockchain.info/charts/avg-block-sizenope, not even close.
Let me give you some actual stats.
Yesterday (Apr 23), there are a total of 130 blocks. Among them, 5 are bigger than 975 KB.
https://www.biteasy.com/blockchain/blocks-date/2015-04-23On Apr 22, there are a total of 152 blocks and only 2 are bigger than 975 KB.
https://www.biteasy.com/blockchain/blocks-date/2015-04-22On Apr 21, there are a total of 153 blocks and 5 are bigger than 975 KB.
https://www.biteasy.com/blockchain/blocks-date/2015-04-21